This invention relates to winglets adapted to reduce the induced drag created by an aircraft""s wings when they create lift. More particularly, it relates to the provision of a winglet that is continuously curved from where it joins the outer end of the wing out to its outer end or tip and the curvature at least closely approximates the curvature of a conical section, viz. has elliptical, parabolic or hyperbolic curvature.
Lifting surfaces (wings) create drag when they create lift. This drag-due-to-lift is called xe2x80x9cinduced drag.xe2x80x9d Aerodynamic theory shows that for essentially planar wings (wings that line essentially in the x-y plane), that the induced drag is minimized if the lift on the wing is distributed elliptically along the span of the wing. That is, the lift per unit span as a function of spanwise position should vary elliptically, with the largest lift per unit span at the wing centerline, and with the lift per unit span gradually dropping in an elliptical manner as the tip is approached. This theoretical result is well known, and many aircraft wings have been constructed with elliptical wing planforms to ensure that the lift does, in fact, vary in an elliptical fashion. The British Spitfire is a classic example of an aircraft wing constructed in an elliptical shape to take advantage of this theoretical result.
The purpose and operation of xe2x80x9cwingletsxe2x80x9d is described in xe2x80x9cAerodynamics, Aeronautics and Flight Mechanicsxe2x80x9d, by Barnes W. McCormick, and published 1979 by John Wiley and Sons, Inc. (pages 215-221). Known winglet constructions in the patent literature are disclosed by U.S. Patents: No. 4,017,041, granted Apr. 12, 1977 to Wilbur C. Nelson; No. 4,190,219, granted Feb. 26, 1980, to James E. Hackett; No. 4,205,810, granted Jun. 3, 1980, to Kichio K. Ishimitsu; No. 4,240,597, granted Dec. 23, 1990, to Roger R. Ellis, W. Martin Gertsen and Norman E. Conley; No. 4,245,804, granted Jan. 20, 1981, to Kichio K. Ishimitsu and Neal R. Van Devender; No. 4,714,215, granted Dec. 22, 1987, to Jeffrey A. Jupp and Peter H. Rees; No. 5,275,358, granted Jan. 4, 1994 to Mark I. Goldhammer and Karela Schippers; No. 5,348,253, granted Sep. 20, 1994 to Lewis B. Gratzer and No. 5,407,153, granted Apr. 18, 1995 to Phillip S. Kirk and Richard Whitcomb.
FIGS. 1-4 of the drawing are identical to FIGS. 1, 2, 4 and 11 in U.S. Pat. No. 5,275,358. Referring to FIG. 1, the aircraft (2) basically comprises an aircraft body (4), left and right wings (6), and a tail section (8). A winglet (10, 110) is shown at the outer end of each wing (6). A coordinate system is defined for the aircraft (2) in the following manner. A longitudinal axis (x) is defined to extend through the center of w the aircraft body (4) in the fore and aft directions. Further, a vertical axis (z) is defined in the up and down directions, while a transverse axis (y) is defined in the left and right directions. The longitudinal axis (x), vertical axis (z) and transverse axis (y) are orthogonal to each other and meet at an origin located at the foremost plane of the aircraft (2).
Referring to FIGS. 2 and 3, a winglet (16), which is generally trapezoidal in shape, is joined to the wingtip (12) so that the winglet (16) upwardly extends from the wing (6). A strake is indicated by reference character (16a) in FIG. 2. The wing (12) (FIG. 2) has upper and lower wing surfaces (18) and (20), a wing leading edge (22), and a wing trailing edge (24). Similarly, the winglet (16) has upper and lower winglet surfaces (26) and (28), a winglet leading edge (30), a winglet trailing edge (32), and a wing/winglet intersection (14). Conventionally, the terms xe2x80x9cupperxe2x80x9d and xe2x80x9clowerxe2x80x9d used in reference to the winglet (16) generally corresponds to the xe2x80x9cinnerxe2x80x9d and xe2x80x9couterxe2x80x9d directions, respectively. This convention will be followed herein. The winglet (16) is swept back at an angle (xcex1) from the vertical z-axis at least equal to the sweep angle of the leading edges of the wings at the wing tip (14) relative to the transverse y-axis (FIG. 2). The winglet (16) is also canted at a cant angle from a plane parallel to the (x) and (y) axis (FIG. 3). Two methods of defining the curvature of the aft portions of the air foils of the wing (12) and winglet (16) are set forth in U.S. Pat. No. 5,275,358, commencing in column 4, at line 7, and continuing into column 5.
FIG. 4 in the drawing is identical to FIG. 11 in U.S. Pat. No. 5,275,358. It is prior art to the present invention and constitutes the invention of Pat. No. 5,275,358. Referring to FIG. 4, the tip of the wing (6) is designated (112). Point (114) is where the wing reference plane (148) intersects the winglet reference plane (150). The winglet (116) is generally trapezoidal in shape. It extends upwardly from the wing tip (112) and the inner section (114). The wing tip (112) has upper and lower wing surfaces (118 and 120), a wing leading edge (122) and a wing trailing edge. The winglet (116) has upper and lower winglet surfaces (126 and 128), a winglet leading edge (130), a winglet trailing edge and a winglet root. Generally, the wing/winglet configuration (110) of U.S. Pat. No. 5,275,358 (FIG. 4) has three primary features. Firstly, the aft portion of the upper wing and winglet surfaces (118 and 129) are flattened to prevent flow separation at the wing/winglet intersection (114). Secondly, the wing and winglet leading edges (122 and 130) are drooped downwardly to prevent premature shockwave development. Thirdly, the winglet (116) is not canted outwardly, so the wing bending moments are not substantially increased by the addition of the winglet (116). These primary features and certain secondary features are described in detail in U.S. Pat. No. 5,275,358.
FIG. 5 of the drawing is identical to FIG. 1B of U.S. Pat. No. 5,348,253. Referring to FIG. 5, what is referred to as xe2x80x9ca blended wingletxe2x80x9d is shown connected to a typical wing end portion (1). The winglet chord equals the wing tip chord at the attachment line (3). A transition section (2) is bounded by the transition line (3) and a chordwise line (4) designating the transition end of the winglet (9). The nearly planar outer portion of the winglet (9) is generally straight from the transition end (4) to the tip (5). A first feature of the FIG. 5 wing/winglet arrangement is a continuous monotonic chord variation bounded by a leading edge curve and a trailing edge curve (8). These curves are tangent to the wing leading edge and trailing edge respectively at the winglet attachment line (3) and are also tangent to the leading edge and trailing edges respectively of the straight section (9) at line (4). The leading edge curve (7) is selected to provide a smooth gradual chord variation in the transition and also, to limit the leading edge sweep angle to less than about 65xc2x0. This is necessary to avoid vortex shedding from the leading edge which would comprise the surface loading and thereby increase drag. The shape of the trailing edge curve (8) is generally not critical but is selected to correspond to the airfoil chord and twist required to achieve optimum loading. This restriction will usually allow the wing and winglet trailing edges to lie in the same plane which is desirable functionally and esthetically.
The second feature is a continuous monotonic variation of cant angle. It is stated that the rate of curvature R must be large enough to accommodate the chord variation in the transition section and allow the practical achievement of optimum aerodynamic loading and minimum interference between wing and winglet. The radius and curvature criteria is given below in terms of a parameter, Kr having fairly narrow limits:             R      h        =                  K        R            ⁢              xe2x80x83            ⁢      cos      ⁢              xe2x80x83            ⁢                        (                                                    φ                4                            2                        +                          π              4                                )                /        cos            ⁢              xe2x80x83            ⁢              φ        4              ;      35     less than           K      R         less than     .50  
where,
h=winglet height measured along a normal to the wing chord plane
xcfx864=cant angle of the planar section
xcex9H=maximum sweep angle of the leading edge curve 7
KR=curvature parameter (select lower limit if practical)
More details respecting the winglet curvature are set forth in U.S. Pat. No. 5,348,253.
The present invention includes the discovery that when winglets are attached to the wing tips, the minimum induced drag is obtained when the lift is distributed in a generally elliptical fashion both in the spanwise and vertical directions. The present invention utilizes winglets having a generally elliptical shape in the z-y plane, assuring that the wing loading closely approximates the ideal lift distribution. This results in minimum induced drag and reduced fuel consumption. The present invention also includes the discovery that the winglets will provide reduced induced drag when the winglets have a generally parabolic shape or a generally hyperbolic shape in the y-z plane.
The present invention includes providing the wings of an aircraft with winglets of a unique curvature. Each wing has an inner end, an outer end, an upper surface, a lower surface, a leading edge and a trailing edge. Each winglet has an inner end, an outer end, an upper surface, a lower surface, a leading edge and a trailing edge. The inner end of each winglet is connected to the outer end of its wing. The upper and lower surfaces of the winglets and the leading and trailing edges of the winglets are continuations of the upper and lower surfaces of the wing and the leading and trailing edges of the wing. Each winglet follows a generally elliptical curve as it extends from its inner end out to its outer end. The generally and said elliptical curve has a major axis that extends substantially perpendicular to the wing reference plane and substantially intersects the location where the outer end of the wing is joined to the inner end of the winglet.
In preferred form, the generally elliptical curve has a minor axis substantially perpendicular to the major axis, and that is spaced above the outer end of the winglet. The minor axis intersects the major axis at a center and a diagonal line extends from the center out to the outer end of the winglet and makes an acute angle of about forty-five to ninety (45xc2x0-90xc2x0) degrees with the major axis.
In preferred form, at its outer end the winglet has a cant angle of substantially about forty-five to about ninety degrees (45xc2x0-90xc2x0).
In preferred form, each wing has a dihedral angle of substantially about zero to fifteen degrees (0xc2x0-15xc2x0).
Other objects, advantages and features of the invention will become apparent from the description of the best mode set forth below, from the drawings, from the claims and from the principles that are embodied in the specific structures that are illustrated and described.